Recall that \(S*T\)  ([1]}) means any linear combination of tensors formed by contraction on \(S\)  and \(T\) . (REF ) can be rewritten as \(\nabla _{\frac{\partial }{\partial t}}A=\nabla ^{2} A+ \sum A*A*A+\tilde{R}(T,T)\) . This form can be generalized into any \(m\) -th covariant derivative \(A\)  for the curve shortening flow \(\mathcal {C}_{t}\) .
